Geodesic
Mathematical modeling of 3D dynamic processes near a fracture using the Schoenberg fracture model
Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 500 (2021), pp. 40-44

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Fractured media are important objects of investigation, because they accumulate oil. Hydraulic fracturing is of great practical interest. The exploration of such heterogeneities with the help of mathematical modeling methods makes it possible to examine different problem formulations with fractures of different forms, sizes, and other characteristics. The Schoenberg fracture model takes into account the characteristics of the fluid inside the fracture, which is utterly important in conducting seismic geological surveys. In this work, an algorithm for computing the medium parameters at the boundary of a fracture described by the Schoenberg model is developed using the grid-characteristic method. We present the results obtained by applying the developed algorithm to the solution of the problem of seismic monitoring of a hydraulic fracture, where the fracture-filling fluid is a necessary part of the investigation.
Keywords: fracture models, seismology, grid-characteristic method, hydraulic fracturing. 
@article{DANMA_2021_500_a7,
     author = {I. B. Petrov and P. V. Stognii and N. I. Khokhlov},
     title = {Mathematical modeling of {3D} dynamic processes near a fracture using the {Schoenberg} fracture model},
     journal = {Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleni\^a},
     pages = {40--44},
     publisher = {mathdoc},
     volume = {500},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DANMA_2021_500_a7/}
}
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I. B. Petrov; P. V. Stognii; N. I. Khokhlov. Mathematical modeling of 3D dynamic processes near a fracture using the Schoenberg fracture model. Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 500 (2021), pp. 40-44. http://geodesic.mathdoc.fr/item/DANMA_2021_500_a7/